# On estimating the probability of aperiodic outbursts of microbial populations from their fluctuating counts

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## Abstract

The irregular sequence of counts of a microbial population, in the absence of observable corresponding environmental changes (e.g., temperature), can be regarded as reflecting the interplay of several unknown or random factors that favor or inhibit growth. Since these factors tend to balance one another, the fluctuations usually remain within bounds, and only by a coincidence—when all or most act in unison—does an ‘outburst’ occur. This situation can be represented mathematically as a sequence of independent random variables governed by a probability distribution. The concept was applied to reported microbial counts of ground meat and wastewater. It is found that the lognormal distribution could serve as a model, and that simulations from this model are indistinguishable from actual records. The parameters of the lognormal (or other) distribution can then be used to estimate the probability of a population outburst, i.e., an increase above a given threshold. Direct estimation of the outburst probability based on frequency of occurrence is also possible, but in some situations requires an impractically large number of observations. We compare the efficiency of these two methods of estimation. Such methods enable translation of irregular records of microbial counts into actual probabilities of an outburst of a given magnitude. Thus, if the environment remains ’stable’ or in dynamic equilibrium, the fluctuations should not be regarded merely as noise, but as a source of information and an indicator of potential population outbursts even where obvious signs do not exist.

## Keywords

Lognormal Distribution Microbial Population Microbial Count Ground Beef Standard Plate Count## Preview

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